Bilayer graphene (\(AB\)  stacked) [1]}, [2]}, [3]}, [4]} (as the other multilayer
2D nanostructures [5]}, [1]}, [7]}, [8]}, [9]}) is of great interest since its
electronic states are considerably richer than those of a monolayer graphene
[10]}, [11]}, [12]}, [13]}. But both single- and multilayer graphene in their
unperturbed state lack the band gap [14]}, [15]}. However, multilayer
graphene materials under the application of a perpendicular electric field
may exhibit the ability to produce an electrically tunable band gap. These
outcomes disclose new possibilities of a much wider range of applications
for graphene materials in electronics and photonics [10]}, [17]}, [18]}, [19]}, [20]}.
Moreover, in the case of\(\ AB\)  stacked bilayer graphene the trigonal warping
effect for the energy spectrum deforms the low-energy excitation
with \(\mathcal {E}\lesssim 10\)  \(\mathrm {meV}\) , which significantly enhances
the rates of the harmonics [4]} in the terahertz region compared to a
monolayer graphene. It takes place the modification of quasi-energy
spectrum, in particular, the induction of valley polarized currents [22]}, [23]}, as well as second- and third- order nonlinear-optical effects
[24]}, [25]}, [26]}, [27]}, [28]} in \(AB\)  stacked bilayer graphene under the
applied intense EM field. So, bilayer graphene (\(AB\)  stacked) has some
advantage as compared to a single layer graphene for the photonic
applications because of its anisotropic zone structure and the extensive
tunable band gap [2]}, [3]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}. The large tunable
band gaps with maximal energy \(U\simeq 280\)  \(\mathrm {meV}\)  [19]} can
make possible to control nonlinear EM response in bilayer graphene at room
temperatures, which is impossible in intrinsic graphene [4]}.
